Is the trajectory constant or not? You are employing a loose definition of the word "constant" to make your case here. Within the "random deviations from the trajectory" could exist several other trajectories, depending on what span of time we're talking about. Within the cluster of those sub-trajectories exists risk if you are a shorter-term trader.
You didn't even know the trajectory was upward until after it had taken place, so to say it was a "risk free" investment is a statement made after the fact, and basically meaningless. Its like making a prediction on 2015's price of bitcoin in 2020. Sure, after the fact, we can say that the overall trajectory was up, and there existed a lot of volatility in the middle. But nobody knew it was a risk-free investment in 2015.
I'm starting to feel like you're trolling me now. What part about "a constant trajectory around which the price oscillates" do you not understand?
Not even going to address the rest of the post until we've established why you refuse to understand this and keep repeating the same wrong thing over and over even when it's pointed out to you.
"Volatility, in essence, is nothing but a random oscillation around a potentially unknown trajectory."
You're talking about a moving average
I am not talking about any moving averages. You could compute them for my example, but they're not relevant to the argument.
Your argument was that volatility is equivalent to risk, which is generally wrong. Neither contains much, if any, information about the other.
To show to you that this is not the case I've tried to give you examples of assets that directly contradict your assertion.
In the 'basket of all stocks' you have no risk in the long-term, because your expected loss (= risk) is strictly negative and hence your expected return is strictly positive, because the realized total return converges towards 10% p.a. (in the case of the US stock market) over time.
Despite that, the asset itself has been volatile. Hence, volatility does not imply anything about risk nor vice versa. The only thing that matters for risk is your strategy and nothing else.
You can have a perpetually flat asset with high risk, or you can have highly volatile assets without any risk (Bitcoin - which does not mean that you are guaranteed to make money).
You can get volatility and risk in any combination and neither implies the other.You are probably conflating risk and actual returns. Risk is a statistical measure, e.g. the expected loss of a strategy, asset or portfolio.
Just like the expected value of a dice roll is 3.5 = 1/6 times sum of all potential results.
With risk the results are potential price trajectories in the market and the probabilities are obviously different and depend on all sorts of parameters.
Realized returns on the other hand are what you end up with in reality, and while risk can give you an idea of a region that you'll land in, it'll never tell you what will really happen for individual 'games'.
Here's another attempt to make the point clear.
Assume you have volatility but it's
always the same. Basically, your price follows a 100% predictable pattern no matter how many people buy or sell. In that case you have volatility, but 100% insight and hence can generate profits without any risk whatsoever.
Obviously this isn't going to happen in real markets (though it does in many games), but it should be sufficiently illustrative to show that volatility and risk aren't related.